I believe you'd only need to buy a game twice, given how the account system works on the Switch. Set it up so the person with the primary account on their console plays the game on a different account, then someone with the secondary account plays it on that one - I've played online multiplayer with a friend by doing that, but logically it'd only work for up to 2 players at once, so you'd need to buy twice to get 4 players in.
As for the suggestion itself, I don't know. The multiplayer games I play on the Switch are usually of the $60, everyone-on-the-same-screen kind.
Hmm. That hasn't worked in the past with Minecraft at least, but I just tested it with Kamiko (only other game I have downloaded to two systems at the moment) and I have it running on both. So yeah, maybe it WILL work, then...